Path Tracking for the Dissipative Chaplygin Sleigh

In this paper we study the problem of path tracking for the Chaplygin sleigh, a well known nonholonomic system. The dynamics and control of a Chaplygin sleigh with dissipation has received much attention in recent years, more so in light of the similarity of its dynamics to that of fish-like swimming. Recent work has shown the existence of limit cycles in the reduced velocity space for a periodically forced Chaplygin sleigh and their use in tracking a reference speed and heading angle for the system. We use these results as our starting point to address the problem of tracking a path for the Chaplygin sleigh. A two part algorithm is proposed; in one part a reference limit cycle in the reduced velocity space is tracked using a harmonic balance method. In the second part we use the idea of a goal point a fixed distance from the vehicle to frame this as a pursuit problem where the sleigh is pursuing the goal point. The two parts of algorithm are coupled. We show that the sleigh is able to simultaneously track a reference path in the plane and with a reference velocity with this approach.